Questions tagged [microeconomics]

Microeconomics is a branch of economics that studies the market behavior of individual actors (usually firms and consumers) and the aggregation of their actions in different institutional frameworks (usually the market).

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132 views

How, with complete markets, do we have a representative agent?

I've read several texts stating that with a complete market assumption, there's always a representative agent lurking. How is it that by assuming complete markets, we're able to prove the existence of ...
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Multidimensional screening and convexity of the surplus/rent function

I'm starting to read the literature of multidimensional screening models for monopolists selling $n$ goods to a continuum of buyers with $m=n$ dimensional types, and Rochet (1987) proves that a ...
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About intertemporal elasticity of substitution

The inter temporal elasticity of substitution between two periods of time is $$\sigma=-\frac{d[\ln(c(s)/c(t))]}{d[\ln(U'(c(s))/U'(c(t)))]}$$ I need to prove that $$\lim_{s \to t}\sigma = -\frac{U'(c(t)...
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Stone-Geary utility function, derivation of Marshallian demand

I am reading a paper on structural change. It has three sectors and it features non homothetic utility function, namely a CES with some thresholds for the consumption of the three goods. The UMP is as ...
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Do assets without rental income streams appreciate relative to assets with rental income streams?

In his book "The Armchair Economist", economist Steve Landsburg critiques an op-ed concerning the relative value of stocks and real estate: James K. Glassman wrote a piece in The New Republic to ...
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why is real wage divided by marginal product of labor often called real marginal cost?

As said in the title, why is real wage divided by marginal product of labor often called real marginal cost? In mathematical formula, $mc_t = (W_t/P_t)/MPN_t$ where $MPN_t$ refers to marginal product ...
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Signalling Model (How to solve a differential equation?)

I'm currently reading "SAVING RATES AND POVERTY: THE ROLE OF CONSPICUOUS CONSUMPTION AND HUMAN CAPITAL" by Omer Moav and Zvika Neeman, and I encounter some problem deriving one of the equations. ...
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131 views

Allocative efficiency — correlation between MB and p in populace with wealth inequality

I was reading a paragraph in an economics textbook that was talking about resource allocation, and felt that it missed an important point, leading to a conclusion that I disagreed with. I was hoping ...
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Utility Representation of Lotteries

We went over a lemma in class leading up to a larger theorem. The Lemma states: Let $\succeq$ be a rational preference relation on $\mathscr{L}$ and let $\succeq$ admit utility representation under ...
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How do supply chains form?

I am trying to put forth a theory for endogenous supply chain formation. A set of $K$ complementary tasks need to be performed to manufacture a good $G$. If manufactured, there exists a demand ...
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Is it possible to have a preference relation that is complete but not transitive?

I've been doing my own reading on non-rational preference relations. Im currently under the impression that transitivity follows as a direct result of completeness of preferences. However my (much ...
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Books for microeconomics and macroeconomics for selected topics

I am a mathematics undergraduate trying to self-learn some economics. I have no background in economics. I wish to know from which chapters of Hal Varian's "Intermediate Microeconomics" (7th edition) ...
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971 views

A few clarifications on Utility equations and indifference curves?

I have the utility equation $U(a,b) = a^{2}b^{3}$ How can I tell if the indifference curves are convex? I was under the impression that if: $U_{a} > 0$ and $U_{b} < 0$ then the curve would ...
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Do discontinuous preferences imply no continuous utility function?

I am trying to think of a preference relation that can be represented by a utility function but such that there does not exist a continuous utility function. I know that you can represent continuous ...
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Meaning of Additively Separable, Linear in X

Often I see both in micro and macro two common terminology : Additively separable. Linear in price or linear in probability. I understand exactly as they sound by looking at the functional form ...
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Is my logic on taxation for this question legit?

At Fenway Park, home of the Boston Red Sox, seating is limited to 39,000. Hence, the number of tickets issued is fixed at that figure. Seeing a golden opportunity to raise revenue, the City of Boston ...
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Math basics for Macro&Micro economics and econometrics

I have just been admitted to a graduate school for studies in economics and I major in public administration during my undergraduate time. I have learnt linear algebra, single variable calculus, ...
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Set Theory Properties of the Budget Constraint

In Microeconomic theory, the budget constraint is defined by 4 distinct properties: It is Bounded Closed Convex Non-empty The 1. 2. and 4. are very straight forward and the benefits in terms of ...
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934 views

Existence of solution to maximization problem

I'm a first year grad student and we're learning about the utility maximization problem and the producer's problem now. We have been assuming that a solution to these problems exists. But every now ...
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748 views

Why labour, capital, and output levels cannot be pinned down in perfect competition?

Consider a firm producing with the following technology: \begin{equation} Y = AL^{\alpha}K^{\beta} \end{equation} Assuming that factors are paid their marginal contribution to output, it can be ...
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Risk Premium in the Expected Utility Theory

Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have $$ Eu(w+x) = u(w+E(x)-R). $$ The classical derivation ...
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Can people lack a comparative advantage and a comparative disadvantage?

Source: Question 9b, p 61, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw = Question 8b in Principles of Microeconomics, 4 Ed, 2008 9. Are the following statements true or false? ...
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Is First Order Stochastic Dominance (FOSD) relation convex?

A convex relation is that $x\succeq y$ implies $\alpha x+(1-\alpha)y\succeq y$. Let $>_{FOSD}$ be $\succ$, is the FOSD convex? Intuitively it seems convex.
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How do I represent this indifference curve graphically?

I am not able to visualize this indifference curve. I consume only two goods: sugar and milk. I will prefer a bundle X of sugar and milk over a bundle Y only if $x_{sugar} > y_{sugar}$, and $x_{...
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857 views

Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)?

My understanding of local non-satiation is that increasing your allocation of one good by a marginal amount increases utility. Suppose your utility takes the following form: $$U(x,y)=x^\alpha y^\beta$$...
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Taxes levied on sellers = Taxes levied on buyers

All page numbers refer to Principles of Microeconomics, 7 Ed, 2014, by NG Mankiw. [p 125:] Taxes levied on sellers and taxes levied on buyers are equivalent. [p 156:] ... When a tax is levied on ...
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Difference between 'surplus' and 'welfare'

I see these two terms used interchangeably but I have the feeling they are not exactly the same. My gut feeling tells me this: 1) Surplus is the additional aggregate utility from the existence of one ...
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How does expected utility theory treat losses?

I've been reading about prospect theory lately and have read often that prospect theory predicts people will be risk averse in gains and risk seeking in losses. This statement is typically ...
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How do you reconcile the Law of Increasing Opportunity Costs and Economies of Scale?

Marginal cost of production always increases, while marginal benefit of production decreases. As far as I understand, that is why the supply curve has positive slope and the demand curve negative ...
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408 views

Quasi-Linear Functions

I understand that quasi-linear functions have a general form $U(x_1,x_2,...,x_n,y) = f(x_1,x_2,...,x_n) + y$ and that for a quasi-linear function, the income effect with respect to the other ...
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General model of economics, economics as mathematical structure

Contrary to the common view, the physics is all about models, there are no such thing as law of nature, because every physical law has its applicability range and therefore all of laws as models. But ...
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Subgame Perfect Equilibrium in Baye, Shin (1999)

The following is taken from Baye, Shin (1999) Consider a contest over a prize valued at 1 with symmetric players $1$ and $2$ who exert a level of effort $x_1$ and $x_2$ respectively. Effort cannot ...
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Self-teaching 1st year PhD Microeconomic Theory

How should one proceed if he wanted to master the microecon theory course typically taught in the 1st year of a PhD program on his own? Which text(s) and/or online course(s) should he follow? Suppose ...
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Are there any examples for $u(x_1, x_2) = \max\{x_1, x_2\}$ in real word?

I know how its graph looks like, and it's like when you want to choose between 2 inferior goods you choose the cheaper one so you can have more, but is there another examples?
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Purpose of a monotonic transformations in utility functions

Based on my economics book, monotonic transformations for a utility function can look something like this: $f(u) = u + 17 $ or even like this: $f(u) = u^3$ That being said what it purpose in the ...
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Modifying Hotelling's lemma: Is this valid?

Hotelling's lemma is stated as: $$\frac{\partial \pi}{\partial p}=y$$ knowing however that on the more basic level, output $y$ is determined by the input(s) $x(p,w)$,let the profit function be ...
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Mixed strategy Nash equilibrium in 3x3 game

What is the MSNE for the following game? I think you can eliminate strategies $A$ for player 1 and $C$ for player $2$, as these will are weakly dominated by all other strategies. Then, the game ...
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The Fed pays 1.50% interest on reserves; so why are interest rates so low?

Since 14th Dec 2017, the Federal Reserve Bank has paid 1.50% interest on excess reserves. So why do depositors' interest rates still remain so low? According to BankRate, across the US, the ...
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Consumer behavior with constrained demand

Suppose there is a linear demand function $D(p)$ describing the demand of an individual consumer. This is derived from a utility function or is just observed, but let us assume it is correct. Now ...
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Separating and supporting hyperplane theorems

I am having trouble understanding the separating and supporting hyperplane theorems. I've read what I can online but am just not able to develop any intuition. Can someone please give a basic outline ...
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Examples of how economists come up with a production function for a firm?

I am a young man studying economics on his own. In every microeconomics text I find, they teach you what a production function is, but they never show examples (or practice problems) on how one comes ...
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Best resources to self-educate myself in economics

I want to learn Economics by myself and I'm looking to build a path with people who're in this field to how and in what order should I learn Economics, I did some research and I've found many ...
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Solving for optimal consumption bundle

Consider a consumer who can consume either A or B, with the quantities being denoted by $a$ and $b$ respectively. If the utility function of the consumer is given by $$-[(10-a)^2+(10-b)^2]$$(suppose ...
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Is there a class of demand functions that deliver equal surplus to consumers and a monopolist?

Consider a market with a monopolist firm that has zero marginal cost and faces demand $D(p;\mathbf{a})$, where $\mathbf{a}$ is a vector of parameters and $p$ is the price. The monopolist maximizes ...
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Are there multiple equilibria in the second price auction?

Suppose that $n\geq 2$ bidders compete in a second price auction. Each bidder $i$ knows their own valuation $v_i$, but only knows the distribution generating the valuations of the other players. ...
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486 views

Bertrand game - Nash equilibrium

The quantity is limited to 300 but the monopoly quantity is equal to 400 and gives a monopoly price of 600. But if we plug the quantity of 300 into the demand function we get a price of 700.But I am ...
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Cournot Competition game with 3 Firms

Three firms are in Cournot competition. The inverse demand curve is denoted p(q) where p is the price if a total of q units are produced. Assumptions are: p(0)>0 and p'(q)<0 and p''(q) $\le 0$ ...
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Paternalistic Government policies

A consumer with income $m$ has preferences $U(x , y) = x^a y^{1-a} $ where a is between 0 and 1. A paternalistic Government wants to regulate the choices of the consumer to maximize it's own welfare ...
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Does the Independence Axiom Require Statistical Independence?

First: Given this definition of the Independence Axiom, If for all $P$, $P'$, $P''$ in the set of lotteries over outcome space $X$, when: $P$ preferred to $P'$ $\implies$ $aP + (1-a)P''$ ...
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Transformation Function

In Mas-Colell microeconomics textbook I have found that profit maximization problem (as well as many further optimization tasks) could be represented with application of some transformation function (...